arXiv:1408.5110math.NT
Large gaps between primes
Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.
Abstract
We show that there exists pairs of consecutive primes less than $x$ whose difference is larger than $t(1+o(1))(\log{x})(\log\log{x})(\log\log\log\log{x})(\log\log\log{x})^{-2}$ for any fixed $t$. Our proof works by incorporating recent progress in sieve methods related to small gaps between primes into the Erdos-Rankin construction. This answers a well-known question of Erdos.
For those who don't wish to read all the news fluff to hear about a mathematical discovery:[1] Abstract. We show that there exists pairs of consecutive primes less than x whose difference is larger than t(1+o(1))(log x)(log log x)(log log log log x)(log log log x)⁻² for any…
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